Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions

Discriminatory Auctions with Resale

We consider multi-unit discriminatory auctions where ex ante symmetric bidders have single-unit demands and resale is allowed after the bidding stage. When bidders use the optimal auction to sell items in the resale stage, the equilibrium in the auction without resale is no longer an equilibrium in an auction with resale. We find a symmetric and monotone equilibrium when there are two units for sale, and, interestingly, we show that there may not be a symmetric and monotone equilibrium if there are more than two units

Welfare-maximizing assignment of agents to hierarchical positions

© 2015 Elsevier B.V. We allocate agents to three kinds of hierarchical positions: top, medium, and low. No monetary transfers are allowed. We solve for the incentive-compatible (IC) mechanisms that maximize a family of weighted social welfares that includes utilitarian and Rawlsian welfares. When the market is tough (all agents bear positive risk of obtaining a low position in any IC and feasible mechanism), then the pseudomarket mechanism with equal budgets (PM) and the Boston mechanism without priorities (BM) yield identical assignments which are always optimal. Otherwise, when the market is mild, PM and BM differ and each one implements the optimal rule under different assumptions on the curvature of virtual valuations. We also establish that both BM and PM mechanisms guarantee IC Pareto-optimal assignments for a domain of preference distributions satisfying weak assumptions

Expertise in online markets

© 2016 INFORMS. We examine the effect of the presence of expert buyers on other buyers, the platform, and the sellers in online markets. We model buyer expertise as the ability to accurately predict the quality, or condition, of an item, modeled as its common value. We show that nonexperts may bid more aggressively, even above their expected valuation, to compensate for their lack of information. As a consequence, we obtain two interesting implications. First, auctions with a "hard close" may generate higher revenue than those with a "soft close." Second, contrary to the linkage principle, an auction platform may obtain a higher revenue by hiding the item's common-value information from the buyers. We also consider markets where both auctions and posted prices are available and show that the presence of experts allows the sellers of high-quality items to signal their quality by choosing to sell via auctions